MinT - Information on Result #858854

Information on Result #858854

Linear OOA(16⁸⁰, 54, F₁₆, 2, 50) (dual of [(54, 2), 28, 51]-NRT-code), using OOA 2-folding based on linear OA(16⁸⁰, 108, F₁₆, 50) (dual of [108, 28, 51]-code), using

discarding factors / shortening the dual code based on linear OA(16⁸⁰, 109, F₁₆, 50) (dual of [109, 29, 51]-code), using
- constructionÂ X applied to AG(F,13P) âŠ‚ AG(F,34P) [i] based on
  1. linear OA(16⁵⁶, 64, F₁₆, 50) (dual of [64, 8, 51]-code), using algebraic-geometric code AG(F,13P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]
  2. linear OA(16³⁵, 64, F₁₆, 29) (dual of [64, 29, 30]-code), using algebraic-geometric code AG(F,34P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
  3. linear OA(16²⁴, 45, F₁₆, 20) (dual of [45, 21, 21]-code), using
    - extended algebraic-geometric code AG_e(F,24P) [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
      - a function field by GarcÃa and Quoos [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.